Geometry

Question Analysis

The main focus is on calculating the area of the given triangle. First, we need to find the height of the triangle using the Pythagorean theorem, and then use the formula  to calculate the area.

 

Key Concept Explanation

The area  of a triangle is calculated by the formula , where  is the base and  is the height. The Pythagorean theorem  (where  is the hypotenuse and ,  are the other two sides) is used to find the unknown side (height in this case) when the hypotenuse and one side of a right - angled triangle are known.

 

Step - by - Step Solution

1. Find the height:

Consider the right - angled triangle on the left side. The hypotenuse is  and the base is . Let the height be . According to the Pythagorean theorem,

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